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Mirrors > Home > ILE Home > Th. List > undifss | Unicode version |
Description: Union of complementary parts into whole. (Contributed by Jim Kingdon, 4-Aug-2018.) |
Ref | Expression |
---|---|
undifss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difss 3108 |
. . . 4
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2 | 1 | jctr 308 |
. . 3
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3 | unss 3156 |
. . 3
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4 | 2, 3 | sylib 120 |
. 2
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5 | ssun1 3145 |
. . 3
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6 | sstr 3016 |
. . 3
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7 | 5, 6 | mpan 415 |
. 2
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8 | 4, 7 | impbii 124 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2612 df-dif 2984 df-un 2986 df-in 2988 df-ss 2995 |
This theorem is referenced by: difsnss 3551 exmidundif 3991 undifdcss 6467 |
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